Efficient nearest neighbor classification using a cascade of approximate similarity measures

This paper proposes a method for efficient nearest neighbor classification in non-Euclidean spaces with computationally expensive similarity/distance measures. Efficient approximations of such measures are obtained using the BoostMap algorithm, which produces embeddings into a real vector space. A modification to the BoostMap algorithm is proposed, which uses an optimization cost that is more appropriate when our goal is classification accuracy as opposed to nearest neighbor retrieval accuracy. Using the modified algorithm, multiple approximate nearest neighbor classifiers are obtained, that provide a wide range of trade-offs between accuracy and efficiency. The approximations are automatically combined to form a cascade classifier, which applies the slower and more accurate approximations only to the hardest cases. The proposed method is experimentally evaluated in the domain of handwritten digit recognition using shape context matching. Results on the MNIST database indicate that a speed-up of two to three orders of magnitude is gained over brute force search, with minimal losses in classification accuracy.